The autohosted application in SharePoint 2013 requires some configuration for using the calouts framework inside the app frame:
1. You need to reference a bunch of javascript files from the hosting portal supporting callouts framework.
2. You need to reference core CSS styles from the hosting portal because they are defining some important properties of the callout markup.

How to Reference the Required Javascript files

Microsoft.Ajax.js

The most base JS file you need to reference is Microsoft.Ajax.js. You don't need a link to this file because the easiest way to render it is to use the ScriptManager control - it renders the content of this file from the embedded resource:

How to get the hosting portal url

In order to reference the callout framework JS files from the hosting portal you need to obtain the portal url. Your app receives it in the "SPHostUrl" parameter in its own url. In ASP.NET it's convenient to save it to the public page property and to reference it from the page markup. Here I save it to the HostWebUrl property:

The required JS files

Now we can easy reference the required files. I've used the debug versions of these files - of course you can use the release (without .debug suffix). Please note that the order of links is important because some of these files depends on another. There are some localized versions of scripts here- you should use the locale of your hosting portal (in my case it is the English one - 1033):